dentify the percentage of change and increase or decrease 75 people to 25 people increase or decrease find the percent of change round to the nearest tenth of a percent
we have that
75 people represent the 100 % so
Applying proportion, find out how much percentage represent the difference (75-25=50)
so
100/75=x/50
solve for x
x=(100/75)*50
x=66.7 %
therefore
Its a decrease and the percentage of change is 66.7%Given that segment AD is congruent to segment BC, and angle DAB is congruent to CBA; Prove: triangle ABE is isosceles
Statement | Reason
AD ≅ BC | Given
∠DAB ≅ ∠CBA | Given
AB ≅ AB | Reflexive property of congruence
ΔADB ≅ ABC | SAS postulate
∠DBA ≅ ∠CAB | CPCTC
ΔABE is isosceles | Any triangle with 2 congruent angles is isosceles
Look at the construction. Which statement is false? XA = YA XP = PY XA = XY
XA = XY is false. XA and YA are both congruent segments, which means they are equal. The same goes for XP and PY.
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a bakery. needs to pack 48 donuts, 12 pastries, and 24 cinnamon in identical quantities across all of the boxes. What is the maximum quantity of boxes she can utilize?
It requires maximum 12 boxes to put 4 donuts, 1 pastry and 2 cinnamon in each box using the Greatest comon factor.
What is Greatest common factor or GCF?The greatest common factor or GCF is the largest number that can be split into exactly two or more other numbers. It is the "best" thing for reducing the complexity of fractions. A factor is a number that, when multiplied by other numbers, produces the desired numbers in mathematics. Factors are another name for the total that results.
The largest factor that two or more numbers have in common is called the greatest common factor (GCF).
It is given that there are 48 donuts, 12 pastries and 24 cinnamon.
Find the greatest common factor of the given values.
Expand 48,12, and 24 in factors.
48= 2x2x2x2x3
12=2x2x3
24=2x2x2x3
Find the greatest common factors of the three factored-out numbers.
GCF=2x2x3=12
So, it requires maximum 12 boxes to put 4 donuts, 1 pastry and 2 cinnamon in each box using the GCF.
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In a horse race with 6 horses, in a horse race you have 6 horses, you make a bet by predicting the ranking of all 6 horses. If you place your bet at random, whatis the probability that you will get the first and second horse correct and in the correct order?Give your answer as a fraction.
Answer
Probability that one will get the first and second horse correct and in the correct order = ½
Explanation
The probability of an event is given as
[tex]\text{Probability of an event = }\frac{Number\text{ of elements in that event}}{Total\text{ number of elements in the sample space}}[/tex]For this question, we need to calculate the probability of getting the first and second horse correctly.
Number of elements in the event = Number of predictions with the first and second horse correct in that order = 1 × 1 × 6 × 5 × 4 × 3 = 360
Total number of elements in the sample space = Total number of possible arrangements for the horses = 6 × 5 × 4 × 3 × 2 × 1 = 720
Probability that one will get the first and second horse correct and in the correct order = (360/720) = ½
Hope this Helps!!!
What is the equation of this graphed line?
To write this equation in slope-intercept form, y = mx + b, we need to find m and b.
m, the slope, is the distance between the points' corresponding y-value divided by the distance between the points' corresponding x-value.
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\m=\frac{6+6}{-7+3}\\m=\frac{12}{-4}\\m=-\frac{12}4\\m=-\frac13[/tex]
b, the y-intercept, is shown as -5, but we can solve for it as well when it is not so easy to tell the value of b. We can solve for b by substituting known solutions of x and y after we find m.
[tex]y=mx+b\\-7=-\frac136+b\\-7=-2+b\\-7+2=-2+2+b\\b=-5[/tex]
So,
[tex]y=-\frac13x-5[/tex]
bookmarksProdigySIS Grades and Attenda...Nearpod - Classifyi...Vocational Assess..G ExploreLe1. The sliders for y= a 2 + b have been set to create the following graph. What are possible values
First we can find the value of b, which is the y-intercept of the function.
Using the point (0, 2), we have that:
[tex]\begin{gathered} y=a|x|+b \\ \\ 2=a\cdot0+b \\ b=2 \end{gathered}[/tex]Now, in order to find the value of 'a', we can use the point (2, -2):
[tex]\begin{gathered} -2=a|2|+b \\ -2=2a+2 \\ 2a=-4 \\ a=-2 \end{gathered}[/tex]So the values of 'a' and 'b' are a = -2 and b = 2.
Determine the coordinates of the midpoint of the segment with given endpoints. J(-3, 2), K(7,10) Midpoint:
The revenue function R in terms of the number of units sold, x, is given as R = 290x-0.52x^2where R is the total revenue in dollars. Find the number of units sold x that produces a maximum revenue?Your answer is x=What is the maximum revenue?$
Solution
Step 1:
The function reaches a maximum where the derivative is equal to 0.
Find the first derivative of the function.
Step 2:
Write the function
[tex]R(x)\text{ = 290x - 0.52x}^2[/tex]Step 3
Find the first derivative
[tex]\begin{gathered} R(x)=\text{ 290x -0.52x}^2 \\ R^{\prime}(x)\text{ = 290 - 1.04x} \end{gathered}[/tex]Step 4:
The function reaches a maximum where the derivative is equal to 0.
[tex]\begin{gathered} 290\text{ - 1.04x = 0} \\ 1.04x\text{ = 290} \\ \text{x = }\frac{290}{1.04} \\ \text{x = 278.8 }\approx\text{ 279} \end{gathered}[/tex]So the number of units which produce the maximum revenue = 279
Step 5:
Substituting this value in the original equation gives the revenue:
[tex]\begin{gathered} R\text{ = 290x - 0.52x}^2 \\ R\text{ = 290}\times279\text{ - 0.52 }\times\text{ 279}^2 \\ R\text{ = 80910 - 42034.14} \\ R\text{ = \$38875.86} \end{gathered}[/tex]Maximum revenue = $38875.86
Find the volume of a cone with a base radius of 5 yd and a height of 9 yd.
Use the value 3.14 for it, and do not do any rounding.
Be sure to include the correct unit in your answer.
yd
A
OT
5 yd
The volume of the cone is 235.5 yd.³
The dimensions of the cone are given as:
Radius of the cone = r = 5 yd.
Height of the cone = h = 9 yd.
π = 3.14
We need to calculate the volume of the cone.
Volume of a cone = 1 / 3 π r² h
Substitute the values , we get that:
V = 1 / 3 (3.14) (5)² (9) yd.³
V = 1 / 3 (3.14) (25) (9) yd.³
V = (3.14) × (25) × (3) yd.³
Simplify the expression:
V = 235.5 yd.³
Therefore, we get that, the volume of the cone is 235.5 yd.³
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drawing and explanation for areaof triangle where h=137 and base = 203
The area of triangle is 13905.5 cm square when height is 137 cm and bae is 203 cm.
Given that,
There is a triangle with height 137 cm and base 203 cm.
We have to find the area of triangle.
We know,
The entire area filled by a triangle's three sides in a two-dimensional plane is referred to as the triangle's area. A straightforward formula can be used to get the area of a triangle by multiplying the sum of the base and height by two.
Area of triangle =1/2×b×h
Area of triangle =1/2×137×203
Area of triangle =1/2×27811
Area of triangle =13905.5
Therefore, The area of triangle is 13905.5 cm square when height is 137 cm and bae is 203 cm.
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Is there enough information given to prove that the following pairs of triangles are congruent? If so, state the postulate or theorem that supports youranswer. If not, state NONE.Word Bank:HL AA CPCTC AAS SSS None SAS
Answer: There is not enough information to conclude they are congruent, NONE.
Explanation
Postulates or theorems
• Hypotenuse Leg (HL) postulate:, when two right triangles have a congruent hypotenuse and a corresponding congruent leg, these are congruent.
,• Angle-Angle (AA) postulate:, two triangles are similar if two corresponding angles are congruent.
,• Corresponding Parts of Congruent Triangles are Congruent (CPCTC): ,when two triangles are congruent, their corresponding sides and angles are also congruent.
,• Angle Angle Side (AAS) Theorem: ,two angles and the non-included side of two triangles are congruent, and if the angles and the side are corresponding parts in each triangle, then the triangles are congruent.
,• Side Side Side (SSS) Postulate: i,f three sides of two triangles are congruent between each other, then the two triangles are congruent.
,• Side Angle Side (SAS) Postulate: ,two angles and the included side of two triangles are congruent, and if the angles and the side are corresponding parts in each triangle, then the triangles are congruent.
We do not know if the sides are congruent as we are not given any information about it, we just know that the three angles are congruent.
Based on the latter, we can conclude that all postulates or theorems involve the congruence of the sides with the exception of AA postulate. However, the AA postulate states that if it is true, the triangles are similar (same shape) but not necessarily congruent (same size).
Therefore, we have not enough information to conclude the triangles are congruent, we would need the to know the congruency of at least one side of both triangles.
I'll give you the pic.
Let's use pythagorean theorem to calculate the remaining side:
[tex]\begin{gathered} c=\sqrt[]{a^2+b^2} \\ c=\sqrt[]{7^2+3^2} \\ c=\sqrt[]{21+9} \\ c=\sqrt[]{30} \end{gathered}[/tex]The area of a square is given by:
[tex]\begin{gathered} A=s^2 \\ \text{Where:} \\ s=\text{One of its sides} \\ A=(\sqrt[]{30})^2 \\ A=30 \end{gathered}[/tex]Equivalent equations have exactly the same solution set. Select Yes or No in thedropdowns to indicate whether each equation is equivalent to this equation.
The given equation is:
[tex]4x+3=\frac{5}{2}x-7[/tex]Solve the equation for x:
[tex]\begin{gathered} 4x+3=\frac{5}{2}x-7 \\ \text{Collect like terms:} \\ \Rightarrow4x-\frac{5}{2}x=-7-3 \\ \Rightarrow\frac{3}{2}x=-10 \\ \Rightarrow3x=-20 \\ \Rightarrow x=-\frac{20}{3} \end{gathered}[/tex]Next substitute the solution into each equation.
The equation that the solution satisfies is equivalent to the original equation.
Check for the first equation:
[tex]\begin{gathered} 4x=\frac{5}{2}x-4;x=-\frac{20}{3} \\ \Rightarrow4(-\frac{20}{3})=\frac{5}{2}(-\frac{20}{3})-4 \\ \Rightarrow-\frac{80}{3}=-\frac{50}{3}-4 \\ \Rightarrow-\frac{80}{3}\ne-\frac{62}{4} \end{gathered}[/tex]Since the solution does not satisfy the equation, it follows that the equation is not equivalent to the original equation.
Hence, select NO for the first equation.
Use the same procedure to check for the other equations.
Only the third and fourth equations are equivalent to the original equation, so feel yes for them, but no for the first and second.
Answer the question below. Be sure to show your work
ANSWER:
We have to find new side-lengths of PQR triangle.
Original sides are.
[tex]\begin{gathered} PQ\text{ = 8cm} \\ QR=17\operatorname{cm} \\ RP=15\operatorname{cm} \end{gathered}[/tex]After multiplying by 2.5 we get
[tex]\begin{gathered} PQ^{\prime}=2.5\times PQ=(8\times2.5)cm=20\operatorname{cm} \\ QR^{\prime}=(17\times2.5)cm=42.5\operatorname{cm} \\ RP^{\prime}=(15\times2.5)cm=37.5\operatorname{cm} \end{gathered}[/tex]These are the new sides of the P'Q'R' triangle.
Sketch the graph of the equation. y= 1/2x− 3/2.
Use the graphing tool to graph the line.
The graph of the line is given below:
What is graph?
The collection of ordered pairings where f(x)=y exists is the graph of a function f. These pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical situation when x and f(x) are real integers.
The graph of the given equation is,
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Hello I am helping my son with independent variable and dependent
It is given that,
As a plane descends, the more time that passes, the lower the plane's altitude is.
So,
Here, x be the time and y the altitude of the plane.
According to the statement, x be the dependent variable and y be the independent variable.
So, the graph is,
which fractions represent how to find the probability to rolling a number less than 5 and a number greater than 2?
Explanation
The probability of an event is the number of favorable outcomes divided by the total number of outcomes possible
Step 1
find the total of favorable possible
[tex]\begin{gathered} \text{for a dice, } \\ a\text{ number less than 5, it is, 1, 2, 3 or 4, ( 4 favorables outcomes}) \\ a\text{ number greater than 2, it is, 3,4 , 5 or 6} \\ \text{the numbers that have the two options are 3 and 4 ( 2 favorable outcomes)} \end{gathered}[/tex]favorable outcomes : 2 ( 3 and 4)
Step 2
find the total number of outcomes possilbe
the dice has 6 faces, (numbers, 1, 2, 3, 4, 5 or 6),
possible outcomes : 6 ( 1,2,3,4,5 and 6)
Step 3
finally replace
[tex]\begin{gathered} P=\frac{favorable\text{ outcomes}}{\text{possible outcomes}} \\ P=\frac{2}{6}=\frac{1}{3} \end{gathered}[/tex] Two different functions are represented by this graph and this table:
Answer
Option B is correct.
Function B has the greater slope.
3 is greater than 2.
Explanation
For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as
[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]For function A, we will pick two points on the line
(x₁, y₁) and (x₂, y₂) are (-2, -1) and (0, 3)
[tex]\text{Slope = }\frac{3-(-1)}{0-(-2)}=\frac{3+1}{0+2}=\frac{4}{2}=2[/tex]For function B, we will pick the two most extreme points on the table
(x₁, y₁) and (x₂, y₂) are (0, 1) and (5, 16)
[tex]\text{Slope = }\frac{16-1}{5-0}=\frac{15}{5}=3[/tex]We can easily see that function B (3) has a greater slope than function A (2).
Hope this Helps!!!
The set consisting of all integers between -2 and -1 will be empty
It is true that the set consisting of all integers between -2 and -1 is empty.
Integers are numbers that are not fraction. They are simply the whole numbers on the number line.
There are positive and negative integers.
Positive Integers are: 1, 2, 3, 4, 5, and so on
Negative Integers are: -1, -2, -3, -4, -5, and so on.
Between -2 and -1, there are no integers. Therefore, the set consisting of all the integers between them is empty.
The equation of the line of best fit of a scatter plot is y = –7x − 2. What is the the y-intercept?
–7
–2
2
7
Answer:
The y-intercept of this line is -2.
A pair of shoes is on sale for 20% off. I paid $95. How much were the shoes originally? Write an equation and solve.
118.75
0.80 * x = 95
x = 95/ 0.80
x = 118.75
With x being the original cost of the shoes.
13. You can afford a $1,800 per month mortgage payment. You've found a 30-year loan at 5.5% interest.(a) How big of a loan can you afford? $(b) How much total money will you pay the bank? $(c) How much of that money is interest? $
Step-by-step explanation:
Given
Principal = $1,800
interest rate = 5.5%
Using the below formula to calculate the mortgage
[tex]\begin{gathered} m\text{ = }\frac{p\cdot\text{ r (}1+r)^n}{(1+r)^n\text{ - 1}} \\ \text{Where P = principal, r = interest rate} \\ m\text{ = \$1800} \\ r\text{ = 5.5\% } \\ r\text{ = }\frac{5.5}{100}\text{ = 0.055} \\ \text{ since it is per month, hence the interest rate is given as} \\ r\text{ = }\frac{0.055}{12}\text{ = 0.00458} \\ n\text{ = 12 }\cdot\text{ 30} \\ n\text{ = 360} \\ 1800\text{ = }\frac{P\cdot0.00458(1+0.00458)^{360}}{(1+0.00458)^{360}\text{ - 1}} \\ 1800\text{ = }\frac{P\cdot0.00458(1.00458)^{360}}{(1.00458)^{360}\text{ - 1}} \\ 1800\text{ = }\frac{P\cdot0.00458\cdot\text{ 5.1812}}{5.1812\text{ - 1}} \\ 1800\text{ = }\frac{P\cdot\text{ 0.0237}}{4.1812} \\ \text{Cross multiply} \\ 1800\cdot\text{ 4.1812 = P }\cdot\text{ 0.0237} \\ 7526.16\text{ = P }\cdot\text{ 0.0237} \\ p\text{ = }\frac{7526.16}{0.0237} \\ P=\text{ \$317, 559. 50} \end{gathered}[/tex]Hence, the loan he can afford is $317, 559. 50
Part B
The total money he will pay to the bank is calculated as follows
Total amount = 1800 * 360
Total amount = $648, 000
You are given the following problem" "A car burns 0.85 gallons of gas per hour when idling. Express this rate in quarts per minute." Which of the given conversion factors will be useful to solve this problem?
Given,
A car burns 0.85 gallons of gas per hour.
We know,
0.85 gallon = 3.4 quartz.
1 hour=60 min.
Thus,
0.85 gallon per hour=3.4/60 quart per min=0.057 quart per min.
Thus the conversion factor is 0.057 quart per min.
which of the following equations represent linear functions? A. x^2+y^2=1 B. x+y=14 C. y=6/x D. y=3(2x+1)
A linear function has this form:
[tex]y=ax+b[/tex]Notice that option A cannot be written in this form, because x and y have a square power. If you clear y you'll get:
[tex]y=\sqrt[]{1-x^2}[/tex]Option B you can write it in the form of a linear equation:
[tex]y=14-x[/tex]For this option, a = -1 and b = 14
Option C cannot be written in this form:
[tex]y=\frac{6}{x}[/tex]And option D can be written like that:
[tex]y=6x+3[/tex]Here, a=6 and b=3.
So, options B and D are linear equations
Express the function graphed on the axes below as a piecewise function.10802-108-6-422246810-10
From the graph it is clear that the function is a horizontal line from -6 to -3 and an oblique line from -3 to 3 so the equation from -6 to -3 is:
[tex]f(x)=5[/tex]The equation of line using two point form from -3 to 3 is found by knowing the points.The line passes through (-2,6) and (0,4) so it follows:
[tex]\begin{gathered} \frac{y-6}{x+2}=\frac{4-6}{0+2} \\ y-6=-(x+2) \\ y=-x-2+6=-x+4 \\ y=f(x)=-x+4 \end{gathered}[/tex]Hence the piecewise function is given by:
[tex]f(x)=\begin{cases}5,-6\leq x<-3 \\ -x+4,-3Hence the function shown above is the required piecewise function.Four students graphed the system of equations shown below. Which graph is correct?
Explanation
Step 1
Let
[tex]\begin{gathered} y_1=-\frac{3}{4}x+4 \\ y_2=\frac{1}{2}x-1 \end{gathered}[/tex]a) graph y1, to draw the line, we need 2 points ( coordinates)so
i)when x=0
[tex]undefined[/tex]CD = 69, BC = 10x + 3. AD = 18x + 44,and AB= 7x- 20. Find BC.
Answer: A) 83
Explanation:
Representing this segments in a number line, and supposing that they are arranged in alphabetical order:
Here we can see that if we sum all of the segments they must be equal to 18x+44:
[tex]7x-20+10x+3+69=18x+44[/tex]Combining like terms:
[tex]17x+52=18x+44[/tex]Now we move all of the terms with x to the right side and all of the independent numbers to the left side:
[tex]\begin{gathered} 52-44=18x-17x \\ 8=x \end{gathered}[/tex]And now that we know the value of x, we can find BC:
[tex]\begin{gathered} BC=10x+3 \\ BC=10(8)+3 \\ BC=80+3 \\ BC=83 \end{gathered}[/tex]Which is option A)
Find the x-intercept and y-intercept of the line. - 6x + 4y= 15 Write your answers as exact values. Do not write your answers as ordered pairs. x-intercept: 1 Х ? y -intercept: 1
The equation of a line is line is given as y = mx + c where m is the slope and c is the y-intercept
From the equation
-6x + 4y = 15
Changing into the form of the general equation
4y = 6x + 15
Divide both sides by 4
y = 6y/4 + 15/4
y = 3y/2 + 15/4
the x intercept is 0 while the y intercept is 15/4.
what has to be true of angles H and K in order for line AB and line CD to be parallel why
When you have two parallel lines like AB and CD and a transversal line like EF you have to know that the angles will be as follow:
All the angles with the color red will be the same between them and the ones in color green will be the same between them because the angles opposite the vertex (the union between two transversal lines) are congruent or equal:
So the answer is:
The angles H and K are equals and the why is the explanation aboveThe order in which you perform operations matters in a numerical expression. O A. True B. False
Answer:
A. True
Explanation:
Consider the numerical expression below:
[tex]9+2\times3[/tex]If we solve from the left to the right, we have:
[tex]9+2\times3=11\times3=33\text{ (Wrong Solution)}[/tex]This result is incorrect.
However, by the order of operations, multiplication comes before addition, so we rightly have:
[tex]9+2\times3=9+6=15[/tex]We see that if we do not follow the order of operations, our results will not be accurate.
Therefore, the order in which you perform operations matters in a numerical expression.
The answer is True.